Two particles P and Q, of masses 0.1kg and 0.3kg respectively, are at rest on a smooth horizontal plane. P is projected directly towards Q with speed 4ums⁻¹. At the same instant, Q is projected directly towards P with speed ums⁻¹. After P and Q collide, P moves with speed 2ms⁻¹ and Q moves with speed 4 ms⁻¹.

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

1. [M1] For use of conservation of momentum once. Must have correct number of terms. Allow g included with all 4 masses and sign errors only.
2. [A1] u=14 Must be positive.
3. [A1] u=10 Must be positive.
4. [M1] For expression or equivalent difference. Allow sign errors only. Using their14 which is the larger of the 2 values found in part (a). If only one value of u found in part (a) then M0. If no value for u substituted, then M0.
5. [A1] Largest loss = 183.6J Allow -183.6, ± 918/5. This mark is dependent on full marks in part (a). Condone negative values for u and v used. If calculating both KE losses, then largest must be chosen for this mark. Condone ±184 CWO.